Defenseman Jack Hillen celebrates an early goal as Washington took a 4-0 lead on Tampa Bay on Saturday. The Capitals needed Mike Green’s goal in overtime to claim their 11th victory in 13 games and a four-point lead in the Southeast Division. (Nick Wass/Associated Press)

Washington Capitals defenseman Jack Hillen practically scoffed at the question of whether he and his teammates have been scoreboard-watching. At this point in the NHL’s regular season, Hillen said, every team in contention for a playoff spot glances at the standings daily, wondering about the various scenarios that could put them over the top.

Only a short time ago, after Washington started this lockout-shortened campaign 2-8-1, few would have predicted the Capitals to be where they are today, atop the Southeast Division with “our destiny in our hand,” according to center Mathieu Perreault.

When March began, the Capitals had the worst record in the Eastern Conference. With six games remaining in the regular season, they might be the hottest team in the league, a trait that could serve them well given the challenging slate that remains.

“We’ve come a long way,” Coach Adam Oates said Saturday night after Washington beat Tampa Bay for its seventh victory in a row and 11th in the past 13 games.

The latest win has provided the Capitals with a valuable four-point cushion over Winnipeg in the chase to win the beleaguered Southeast Division and claim the No. 3 playoff seed in the Eastern Conference. It also could come in handy given the teams’ schedules over the final stretch.

The Jets are in the midst of a three-game winning streak after losing five contests in a row earlier this month. They have just two games left against opponents that would qualify for the postseason if it started Sunday, and four of their final six games are at home.

The Capitals, meanwhile, have five games against four of the Eastern Conference’s top six teams, starting Tuesday night at home against Toronto. Their other remaining contest is against Winnipeg on April 23 at Verizon Center, a matchup that should loom large since either team could be left out of the playoffs if it does not win the division.

“We’ve got to keep going. It’s one of those things that they’re going to keep pressing, we’re going to keep pressing,” forward Jason Chimera said. “Winnipeg’s got a lot of home games and stuff like that. We know that. We know where we are. We’ve been playing really well these last couple games to get us here, and so we’ve just got to keep our foot on the pedal.”

But beating the NHL’s elite has been an issue for Washington this season. Its recent hot streak has included just one win in regulation over a playoff team (Tuesday in Montreal), the team’s first such victory in 2013.

For the year, the Capitals were just 4-12 against the Eastern Conference’s top eight teams through Sunday, with three of the wins coming via shootout. Fourteen of their 23 victories have come against foes from the Southeast Division, considered to be the worst in the NHL.

“I hope playing different teams is going to help us,” captain Alex Ovechkin said. “But again, it’s all about us right now. We just have to keep winning and keep going.”

This newfound fortitude, the result of the team’s recent success, has invigorated Washington’s locker room now that qualifying and advancing in the playoffs has become a tangible goal again. And given the early struggles these players have overcome, faltering down the stretch against some of the league’s best teams would be a disappointment.

“We want to win them all. We want to progressively get better each game going into the playoffs and that’s it,” defenseman Mike Green said. “It’s taken us some time with the situation we had at the beginning of the year with no camp, new coach, new system, new players. It’s taken us some time to adjust, but we’ve collectively come together as a group and jelled and it just took that long to get our feel.”